Optimal measurement problem for a stochastic distributed parameter system with movable sensors

Abstract

Abstract This paper deals with the problem of determining optimal measurements for a stochastic distributed parameter system (DPS). This problem can be formulated as an optimal control problem for a system described by the Riccati equation, whose solution gives, generally a measurement strategy of the scanning type. However, the specified strategy is not always practicable, and therefore a more realistic formulation is required. The optimal measurement problem is reformulated as that of minimizing not only the trace of the estimation error covariance, but also the total kinetic energy of the measurement sensors by taking the sensor velocity as the control variable. The existence of an optimal solution for the reformulated problem is proved, and the necessary conditions for optimality are derived in the form of the matrix minimum principle. Based on successive approximation of the Riccati equation, a computationally advantageous approach is developed to obtain the optimal measurement of the scanning type w...